Mirror modifier creates new vertices in weird ways
The Mirror Modifier, unless it's configured differently, mirrors a mesh around the Object Origin. It duplicates any geometry on the other side.

Usually you shouldn't cross the mirror glass. But when you add the default cube, 4 verts are left of the O.O. and the other 4 are right of the O.O. So it's not the best place to start.

Here are the 4 stages, shown with cubes:


Every vertex is on the left side of the middle, everythings fine.
4 verts are left and 4 verts are in the middle. That's where clipping comes in. It will glue any verts to the middle that try to cross it. It doesn't repair any tresspassing. Be careful when you do that with a cube. It will trap a face in the middle which can lead to unclean topology.
That one's not too healthy: most cubes are on the left side but one is on the right side. You can do that but it requires more attention.
That one causes sort of bad geometry. the original and the mirrored mesh intersect, edges are crossing the line. z-fighting can occur when the faces are parallel to the mirror axis.


Now, technically you can do any of that, you just have to be careful not to cause unwanted effects.